Notice how Chrome actually also shows occurrences of “ae” when searching for “æ”.
The same thing goes when searching for “Ø”, “Ö” or similar accents: They will show occurences of “o”.
Usability wise, I think this is a rather good principle for end-user solutions, just like Google Chrome. But, but. As an advanced user, i would like to know if i can turn it off? Not as a general setting. Because the usecase would be that you search, and find too much. Based on this, if you search for something with accented characters, a new checkbox should appear. My suggestion (mockup):
This way, you will start with a “wide” search and end up being able to filter in more correctly.